Question

Which are the solutions of x2 = –13x – 4? 0, 13 0, –13 StartFraction 13 minus StartRoot 153 EndRoot Over 2 EndFraction comma StartFraction 13 + StartRoot 153 EndRoot Over 2 EndFraction StartFraction negative 13 minus StartRoot 153 EndRoot Over 2 EndFraction comma StartFraction negative 13 + StartRoot 153 EndRoot Over 2 EndFraction

Answer 1

`x_(1)=(-13+√(153))/(2)\\x_(2)=(-13-√(153))/(2)`

Explanation:

The given expression is

`x^(2)=-13x-4`

To solve this quadratic equation, we first need to place all terms in one side of the equation sign

`x^(2) +13x+4=0`

Now, to find all solutions of this expression, we have to use the quadratic formula

`x_(1,2)=\frac{-b\±\sqrt{b^(2)-4ac}}{2a}`

Where
`a=1`,
`b=13` and
`c=4`

Replacing these values in the formula, we have

`x_(1,2)=\frac{-13\±\sqrt{(13)^(2)-4(1)(4)}}{2(1)}\\x_(1,2)=(-13\±√(169-16))/(2)=(-13\±√(153))/(2)`

So, the solutions are

`x_(1)=(-13+√(153))/(2)\\x_(2)=(-13-√(153))/(2)`

If we approximate each solution, it would be

`x_(1)=(-13+√(153))/(2)\approx -0.32\\\\x_(2)=(-13-√(153))/(2) \approx -12.68`

Answer 2

D on Edge

Explanation: